Plane construction from 3D Points in OpenCV

Question

I would like to construct a plane from a list of 3D points in OpenCV. I would like to obtain the result by finding the four parameters in the following form: Ax+By+Cz+D = 0. Would anyone suggest me a way to do it?

principal component analysis should give good results in theory. I'd suggest you a simple RANSAC method though. You should present a 3D image of your points to give an idea about your setting. — Micka, Nov 30 '15 at 11:23
So see my answer it is going to solve the problem, you may ask about any ambiguity. — Humam Helfawi, Nov 30 '15 at 13:10

Humam Helfawi · Accepted Answer · 2018-02-01T11:29:57.203

4

If the data does not contain outliers and does not contain more than one plane. Furthermore, all the points lay exactly on a plane (the data is not noisy), it is so simple:

Pick up three random points which are not lay on the same line.
solve this system of linear equations:

x1+by1+cz1+d = 0
x2+by2+cz2+d = 0
x3+by3+cz3+d = 0

then :

A= Choose any number you want in order to match your scale. 
B= b*A 
C= c*A 
D= d*A

If the data is noisy or contains outliers or more than plane (or both) you need then some kind of Robust Estimation techniques. Search for RANSAC as a start.

if you are familar with RANSAC you can see this example here (it is about lines you can simply generlize it to deal with plane)

edited Feb 01 '18 at 11:29

answered Nov 30 '15 at 11:23

Humam Helfawi

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Finally, I find a way by using the class SVD to solve the problem. First I transform the equation of plane from `AX+BY+CZ+D = 0` to `A'X+B'Y+C' = Z`, so the required parameters to characterize a plane becomes 3. Then by applying `SVD sample(leftMatrix); sample.backSubst(z, result);` where leftMatrix is a n*3 matrix containing each row (x_i, y_i, 1), z is just all the points of z coordinates in n*1 matrix form, variable"result" finally conotains the calculated plane parameters. – Carl Dec 10 '15 at 13:31
Anyway, thank you for your answer as your answer inspried me to reach my current solution. – Carl Dec 10 '15 at 13:35
1

glad it helped. You may accept this answer or try to write a full answer by yourself and accept your own. good luck – Humam Helfawi Dec 10 '15 at 13:37

score 1 · Answer 2 · answered May 06 '20 at 05:43

Answer by leveraging OpenCV

If you want to have equation solved by 3 points, just like follows:

ax + by + cz = 1

Example

you have three points: cv::Point3f p1, p2 and p3, and here is the code:

cv::Matx33f M(p1.x, p1.y, p1.z,
              p2.x, p2.y, p2.z,
              p3.x, p3.y, p3.z);
cv::Vec3f d(1, 1, 1);
cv::Vec3f coef = M.inv() * d;

Then, a, b, c are coef(0), coef(1), coef(2) sequentially.

Plane construction from 3D Points in OpenCV

2 Answers2

Answer by leveraging OpenCV

Example

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